本书包含超过两个学期的研究生水平的抽象代数课程所需的足够的材料，代数数论的介绍，和代数几何的基本知识。本书适合对代数感兴趣的研究生和数学研究人员阅读参考。 This book, based on a first-year graduate course the author taught at the University of Wisconsin, contains more than enough material for a two-semester graduate-level abstract algebra course, including groups, rings and modules, fields and Galois theory, an introduction to algebraic number theory, and the rudiments of algebraic geometry. In addition, there are some more specialized topics not usually covered in such a course. These include transfer and character theory of finite groups, modules over artinian rings, modules over Dedekind domains, and transcendental field extensions. This book could be used for self study as well as for a course text, and so full details of almost all proofs are included, with nothing being relegated to the chapter-end problems. There are, however, hundreds of problems, many being far from trivial. The book attempts to capture some of the informality of the classroom, as well as the excitement the author felt when taking the corresponding course as a student.

前辅文
PART ONE Noncommutative Algebra
  CHAPTER 1 Definitions and Examples of Groups
  CHAPTER 2 Subgroups and Cosets
  CHAPTER 3 Homomorphisms
  CHAPTER 4 Group Actions
  CHAPTER 5 The Sylow Theorems and p-groups
  CHAPTER 6 Permutation Groups
  CHAPTER 7 New Groups from Old
  CHAPTER 8 Solvable and Nilpotent Groups
  CHAPTER 9 Transfer
  CHAPTER 10 Operator Groups and Unique Decompositions
  CHAPTER 11 Module Theory without Rings
  CHAPTER 12 Rings, Ideals, and Modules
  CHAPTER 13 Simple Modules and Primitive Rings
  CHAPTER 14 Artinian Rings and Projective Modules
  CHAPTER 15 An Introduction to Character Theory
PART TWO Commutative Algebra
  CHAPTER 16 Polynomial Rings, PIDs, and UFDs
  CHAPTER 17 Field Extensions
  CHAPTER 18 Galois Theory
  CHAPTER 19 Separability and Inseparability
  CHAPTER 20 Cyclotomy and Geometric Constructions
  CHAPTER 21 Finite Fields
  CHAPTER 22 Roots, Radicals, and Real Numbers
  CHAPTER 23 Norms, Traces, and Discriminants
  CHAPTER 24 Transcendental Extensions
  CHAPTER 25 The Artin-Schreier Theorem
  CHAPTER 26 Ideal Theory
  CHAPTER 27 Noetherian Rings
  CHAPTER 28 Integrality
  CHAPTER 29 Dedekind Domains
  CHAPTER 30 Algebraic Sets and the Nullstellensatz
Index